question_answer

How many triangles are there altogether in the given figure?

A)  14      

B)  12

C)  10                  

D)  8

Correct Answer: A

Solution :

            [a] The figure may be labelled as shown.

The simplest triangles are AHG, AIG, AIB, JFE, CJE and CED i.e. 6 in number.

The triangles composed of two components each are ABG, CFE, ACJ and EGI i.e. 4 in number.

The triangles composed of three components each are ACE, AGE and CFD i.e. 3 in number.

There is only one triangle i.e. AHE composed of four components.

Therefore, there are 6+4+3+1=14 triangles in the given figure.